Abstract : —We consider a slow fading two-hop relay channel where a source terminal communicates with a destination through a layer of relays without a direct link. First, we introduce the notion of time-varying distributed rotation and propose a linear relaying scheme called rotate-and-forward (RF). The main idea is to create a time-varying channel and to convert the spatial diversity to time diversity. It is shown that this scheme achieves the optimal diversity-multiplexing tradeoff (DMT) of the channel with full-duplex relays. While more involved non-linear relaying schemes previously proposed in the literature are optimal in the same setting, we show here that simple linear relaying can also be DMT optimal. Then, we extend the RF scheme to the relay channel with multiple hops where the DMT optimality of the two-antenna case is shown. Finally, we apply the idea of distributed rotation to the decode-and-forward relays. Same diversity order as previous schemes can be achieved with low signaling complexity.